Restricted Values f(x) g(x) h(x) x x x

Slides:



Advertisements
Similar presentations
Definition of Limit Lesson 2-2.
Advertisements

Rational Functions 8-4 Warm Up Lesson Presentation Lesson Quiz
A Dash of Limits. Objectives Students will be able to Calculate a limit using a table and a calculator Calculate a limit requiring algebraic manipulation.
EXAMPLE 3 Simplify an expression by dividing out binomials Simplify x 2 – 3x – 10 x 2 + 6x + 8. State the excluded values. SOLUTION x 2 – 3x – 10 x 2 +
Key Concept 1. Example 1 Operations with Functions A. Given f (x) = x 2 – 2x, g (x) = 3x – 4, and h (x) = –2x 2 + 1, find the function and domain for.
5-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz
Solving Quadratics by Completing the Square, continued Holt Chapter 5 Section 4.
Graphs of Functions Defined by Expressions in a Linear Equation On a standard screen, graph the following functions, determined from the given linear equation:
Warm-up Arithmetic Combinations (f+g)(x) = f(x) + g(x) (f-g)(x) = f(x) – g(x) (fg)(x) = f(x) ∙ g(x) (f/g)(x) = f(x) ; g(x) ≠0 g(x) The domain for these.
Evaluating Limits Analytically Lesson What Is the Squeeze Theorem? Today we look at various properties of limits, including the Squeeze Theorem.
Limit Laws Suppose that c is a constant and the limits lim f(x) and lim g(x) exist. Then x -> a Calculating Limits Using the Limit Laws.
6-8 Transforming Polynomial Functions Warm Up Lesson Presentation
Objectives Define and use imaginary and complex numbers.
A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.
8.4: Do Now: Multiply the expression. Simplify the result.
EXAMPLE 2 Multiply rational expressions involving polynomials Find the product 3x 2 + 3x 4x 2 – 24x + 36 x 2 – 4x + 3 x 2 – x Multiply numerators and denominators.
Product and Quotients of Functions Sum Difference Product Quotient are functions that exist and are defined over a domain. Why are there restrictions on.
Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Combinations of Functions; Composite Functions.
1 Solve each: 1. 5x – 7 > 8x |x – 5| < 2 3. x 2 – 9 > 0 :
To remember the difference between vertical and horizontal translations, think: “Add to y, go high.” “Add to x, go left.” Helpful Hint.
Holt Algebra Solving Quadratic Equations by Graphing and Factoring A trinomial (an expression with 3 terms) in standard form (ax 2 +bx + c) can be.
Restricted Values 1. Complete the table of values for the given rational functions. x xx Determine the restricted.
1 Beginning & Intermediate Algebra – Math 103 Math, Statistics & Physics.
 A rational function is one that can be expressed as a ratio of two polynomials.  Some examples: y =, f(x) =, g(x) =, h(x) =  Here are some.
Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Combinations of Functions; Composite Functions.
Restricted Values 1. Complete the following tables of values for the given radical functions: x of 2 Chapter.
Function Notation Find function values using f(x) notation or graphs.
Function Notation Assignment. 1.Given f(x) = 6x+2, what is f(3)? Write down the following problem and use your calculator in order to answer the question.
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, GeorgiaAdapted from Various SourcesMCC9-12.F.IF.7b.
5.3 and 5.4 Solving a Quadratic Equation. 5.3 Warm Up Find the x-intercept of each function. 1. f(x) = –3x f(x) = 6x + 4 Factor each expression.
7.3: Addition and Subtraction of Rational Expressions
Many quadratic equations contain expressions that cannot be easily factored. For equations containing these types of expressions, you can use square roots.
5-3 Solving Quadratic Equations by Graphing and Factoring Warm Up
Summarize the Rational Function Task
Combining Like Terms 8th Pre-Algebra.
3.3 Properties of Logarithmic Functions
6-8 Transforming Polynomial Functions Warm Up Lesson Presentation
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
What Do Limits Have To Do With Calculus?
Evaluating Limits Analytically
Chapter 7 Functions and Graphs.
26 – Limits and Continuity II – Day 2 No Calculator
Summarize the Rational Function Task
Evaluating Limits Analytically
Objectives Solve quadratic equations by graphing or factoring.
Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9 3
Partner Whiteboard Review.
Factoring Special Cases
Chapter 3 Section 6.
Graph the function, not by plotting points, but by starting with the graph of the standard functions {image} given in figure, and then applying the appropriate.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
5 minutes Warm-Up Solve. 1) 2) 3) 4).
Chapter 3 Section 6.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7
VOCABULARY! EXAMPLES! Relation: Domain: Range: Function:
Function Notation. Function Notation What is function notation? Function notation is another way to write “y=“ The notation looks like this: f(x) f(x)
Restricted Values f(x) g(x) x x h(x) j(x) x x 1 of 2
26 – Limits and Continuity II – Day 1 No Calculator
The Indeterminate Form
27 – Graphing Rational Functions No Calculator
Find the derivative of the following function:   {image} .
Warm-up 5/22/2019 Day 6.
Function Notation. Function Notation What is function notation? Function notation is another way to write “y=“ The notation looks like this: f(x) f(x)
Function Notation. Function Notation What is function notation? Function notation is another way to write “y=“ The notation looks like this: f(x) f(x)
Warm-Up Honors Algebra /17/19
Write each expression by using rational exponents.
Calculator Check for Equivalence of Simplified Expressions
Calculator Check for Equivalence of Simplified Expressions
Presentation transcript:

Restricted Values f(x) g(x) h(x) x x x Chapter 12 Discovery 1 Restricted Values 1. Complete the table of values for the given rational functions. f(x) g(x) h(x) x x x -3 -2 -1 1 2 3 -3 -2 -1 1 2 3 -3 -2 -1 1 2 3 Determine the restricted values of each function. 1 of 2

Chapter 12 Discovery 1 Restricted Values 2. Graph the given rational functions on a calculator screen, (-9.4, 9.4, 1, -6.2, 6.2, 1, 1). Trace each function’s graph. What happens when you reach the point on a graph for the restricted x-values found in exercise 1? Write a rule for determining the restricted values of a rational function by viewing its table of values. function by viewing its graph. function algebraically. 2 of 2

Simplified Expressions and Chapter 12 Discovery 2 Simplified Expressions and Restricted Values To simplify complete the following steps: Factor out the GCF, 2x. Rewrite the GCF as 1. 1 of 2

Simplified Expressions and Chapter 12 Discovery 2 Simplified Expressions and Restricted Values Check the equivalence of the expressions and by graphing. Let and 1. Both graphs appear to be coinciding. However, look at the table of values for x = -3, -2, -1, 0, 1, 2, and 3. What do you see? 2. Determine the restricted values for each expression. 3. Explain why the two expressions are equivalent for all values except when x = 0. 2 of 2